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Omni-MATH / Consider an unusual biased coin, with probability p of landing heads, probability q≤p of landing tails, and probability ……

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problem

Consider an unusual biased coin, with probability pp of landing heads, probability q≤pq \leq p of landing tails, and probability \frac{1}{6}oflandingonitsside(i.e.onneitherface).Itisknownthatifthiscoinisflippedtwice,thelikelihoodthatbothflipswillhavethesameresultis12 of landing on its side (i.e. on neither face). It is known that if this coin is flipped twice, the likelihood that both flips will have the same result is \frac{1}{2}. Find pp.
Plain-text mathematical notation (without MathML)
Consider an unusual biased coin, with probability p of landing heads, probability q≤p of landing tails, and probability \frac{1}{6}oflandingonitsside(i.e.onneitherface).Itisknownthatifthiscoinisflippedtwice,thelikelihoodthatbothflipswillhavethesameresultis(1)/(2). Find p.
Original LaTeX notation
Consider an unusual biased coin, with probability $p$ of landing heads, probability $q \leq p$ of landing tails, and probability \frac{1}{6}$ of landing on its side (i.e. on neither face). It is known that if this coin is flipped twice, the likelihood that both flips will have the same result is \frac{1}{2}$. Find $p$.

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Source and history

task_id
3927dcae-5d8d-5b58-9ac4-0d3ca78b8e16
task_key
test--3927dcae-5d8d-5b58-9ac4-0d3ca78b8e16
task_revision_id
1
config / split
/ test

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